# Francesca Tombari: Vietoris-Rips complexes in TDA and their decompositions

**Time: **
Fri 2019-10-11 13.00 - 14.00

**Location: **
Room 3418, Lindstedtsvägen 25, 4th floor, Department of Mathematics, KTH

**Participating: **
Francesca Tombari

The aim of topological data analysis (TDA) is to study

datasets using tools from algebraic topology. The step zero in this

process is to put some geometrical structure on the dataset we want to

analyze. Interpreting a dataset as a pseudo-metric space, one can build

the Vietoris-Rips complex, a filtered simplicial complex whose vertices

are the data-points. The goal of this talk will be to familiarize with

Vietoris-Rips complexes, give results about their decompositions from a

homotopical point of view, and see how they are actually direct

consequences of more general statements about simplicial complexes.